Chapter 3
Kinetics of Particles
Introduction
Kinetics is the study of the relations between unbalanced force and the resulting changes in motion, i.e. F vs r, v, a.
The three approaches
A. Direct Application or Force-Mass-Acceleration
B. Work and Energy
C. Impulse and Momentum
Special Applications
Impact
3. Kinetics of Particles
3-1 Force, Mass,
and Acceleration
The main equation is the Newton’s second law.
Combine it with coordinate systems studied in Chapter 2 to solve engineering problems
Example
3-1. Force, Mass, and Acceleration
Newton’s second law
3-1. Force, Mass, and Acceleration
Constrained and Unconstrained Motions
Unconstrained motion: No mechanical guides or linkages to constrain its motion. Ex. airplanes, rockets, etc.
Constrained motion: Motion is limited by some mechanical guide or linkages. Ex. mechanisms
Free Body Diagram
3-1. Force, Mass, and Acceleration
A free-body diagram must be drawn to correctly evaluating all forces involved in Newton’s second law.
Procedures
Clearly draw an isolated body
Define coordinate system and their positive directions
Add all the forces (contact and non-contact) acting on that body
Rectilinear vs Curvilinear
3-1. Force, Mass, and Acceleration
Example 1: A log and a pulley
3-1. Force, Mass, and Acceleration
Ans: 4.62 m/s
Example 2: An accelerometer
3-1. Force, Mass, and Acceleration
Example 3: A Conveyor
3-1. Force, Mass, and Acceleration
Ans: N = 3mgsin(θ), ω=√(2gR) /r
Example 4: A Conical dish
3-1. Force, Mass, and Acceleration
Ans: 3.41 ≤ ω ≤ 7.21 rad/s
Example 5: A car on a curve
3-1. Force, Mass, and Acceleration
Ans: 7.83 kN, 11.34 kN, 7.83 kN
